Length-scale ill conditioning in linear-scaling DFT

We discuss the problem of searching for the electronic ground state in linear-scaling DFT techniques, with particular attention to the pseudopotential scheme embodied in the CONQUEST code. An important source of difficulty in the groundstate search is ill conditioning associated with the different dependence of the total energy on wavefunction variations at different length scales. We recall how this 'length-scale ill conditioning' is handled by preconditioning in conventional plane-wave methods, and we show that analogous preconditioning schemes can be derived in the linear-scaling framework. We present the results of practical tests which show that the proposed preconditioning gives a substantial speed-up in convergence to the ground state. (C) 1998 Elsevier Science B.V.